A.B.R.β
First Battle
The second in the A.B.R. series of guardians, this boss is encountered inside the Singing Hill, right before getting the Hymn Crystal Purger. As noted in the description and in its ability table, this monster is the sole possessor of the Red Magic Absorption passive skill, which allows it to absorb all Red Magic casted against it, rendering all offensive Song Magic useless. Due to that, all of the damage output will have to come from your vanguards, while Aurica takes a support role, using her Blue Magic songs to heal and buff the party, which is also the only way you have for raising Harmonics in this battle.
As for its other skills, aside of being immune to status changes, the A.B.R.β has the following attacks: Rock Cannon, which deals average physical damage in addition to lowering its target's defense; Ring Bit, which deals large physical damage to all vanguards; and finally, High Buster, which deals large physical damage to a single target. As indicated above, you will have to use your Vanguards to attack it, so let loose the best skills and attack items you have at the moment, while you let Aurica handle all the healing with her Life Warmth song, and if she has learned them, allow her to occasionally buff your party with her various Guardian songs. However, don't kill it too quickly, as you'll need some time to fill the Limit Gauge twice in order to achieve full Harmonics with only Blue Magic.
Second Battle
Main article: A.B.R.